<h2>Problem 218</h2>
<div style="color:#666;font-size:80%;">22 November 2008</div><br />
<div class="problem_content">
<p>Consider the right angled triangle with sides a=7, b=24 and c=25.
The area of this triangle is 84, which is divisible by the perfect numbers 6 and 28.<br />
Moreover it is a primitive right angled triangle as gcd(a,b)=1 and gcd(b,c)=1.<br />
Also c is a perfect square.</p>

<p>We will call a right angled triangle perfect if<br />
-it is a primitive right angled triangle<br />
-its hypotenuse is a perfect square</p>

<p>We will call a right angled triangle super-perfect if<br />
-it is a perfect right angled triangle and<br />
-its area is a multiple of the perfect numbers 6 and 28.
</p>

<p>How many perfect right-angled triangles with c<img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' />10<img src="" style="display:none;" alt="^(" /><sup>16</sup><img src="" style="display:none;" alt=")" /> exist that are not super-perfect?</p>

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